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A train runs along an unbanked circular track of radius 30 m at a speed of 54 km/h. The mass of the train is 106 kg. What is the angle of banking required to prevent wearing out of the rail ?
- a)27∘
- b)36.8∘
- c)42∘
- d)32∘
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A train runs along an unbanked circular track of radius 30 m at a spee...
Given:
Radius of the circular track, r = 30 m
Speed of the train, v = 54 km/h = 15 m/s
Mass of the train, m = 106 kg
To find:
Angle of banking required to prevent wearing out of the rail.
Solution:
Let θ be the angle of banking required.
The centripetal force required for the train to move in a circular path is given by,
F = mv²/r
where,
m = mass of the train
v = velocity of the train
r = radius of the circular track
The gravitational force acting on the train is given by,
mg
where,
m = mass of the train
g = acceleration due to gravity
The normal force acting on the train is given by,
N = mg cosθ
where,
θ = angle of banking
mg sinθ = mv²/r
sinθ = v²/(rg) = (15²)/(30×9.8) = 0.7653
θ = sin⁻¹(0.7653) = 37°
Therefore, the angle of banking required to prevent wearing out of the rail is 37°. Answer: (b)
Radius of the circular track, r = 30 m
Speed of the train, v = 54 km/h = 15 m/s
Mass of the train, m = 106 kg
To find:
Angle of banking required to prevent wearing out of the rail.
Solution:
Let θ be the angle of banking required.
The centripetal force required for the train to move in a circular path is given by,
F = mv²/r
where,
m = mass of the train
v = velocity of the train
r = radius of the circular track
The gravitational force acting on the train is given by,
mg
where,
m = mass of the train
g = acceleration due to gravity
The normal force acting on the train is given by,
N = mg cosθ
where,
θ = angle of banking
mg sinθ = mv²/r
sinθ = v²/(rg) = (15²)/(30×9.8) = 0.7653
θ = sin⁻¹(0.7653) = 37°
Therefore, the angle of banking required to prevent wearing out of the rail is 37°. Answer: (b)
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